Descriptor-based methods of electrochemically measuring an analyte as well as devices, apparatuses and systems incorporating the same

ABSTRACT

Methods are disclosed for measuring an analyte concentration in a fluidic sample. Such methods allow one to correct and/or compensate for confounding variables such as hematocrit, salt concentration and/or temperature before providing an analyte concentration. The measurement methods use response information from a test sequence having at least one DC block, where DC block includes at least one excitation pulse and at least one recovery pulse, and where a closed circuit condition of an electrode system is maintained during the at least one recovery pulse. Information encoded in the excitation and recovery pulses are used to build within- and across-pulse descriptors to correct/compensate for hematocrit, salt concentration and/or temperature effects on the analyte concentration. Methods of transforming current response data also are disclosed. Further disclosed are devices, apparatuses and systems incorporating the various measurement methods.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a divisional of U.S. patent application Ser.No. 14/852,044 (filed 11 Sep. 2015), which subsequently issued as U.S.Pat. No. 10,295,494, which is a continuation of Int'l Patent ApplicationNo. PCT/EP2014/054956 (filed 13 Mar. 2014), which claims priority to andthe benefit of U.S. Provisional Patent Application No. 61/801,321 (filed15 Mar. 2013). Each patent application is incorporated herein byreference as if set forth in its entirety.

TECHNICAL FIELD

This disclosure relates generally to mathematics and medicine, and moreparticularly, it relates to methods of electrochemically measuring ananalyte in a fluidic sample based upon an algorithm incorporatingacross- and within-pulse descriptors derived from AC and/or DC responseinformation of an electrical test sequence.

BACKGROUND

Significant benefits can be realized from electrochemically measuringanalytes in fluidic samples (i.e., biological or environmental). Forexample, individuals with diabetes can benefit from measuring glucose.Those potentially at-risk for heart disease can benefit from measuringcholesterols and triglycerides among other analytes. These are but a fewexamples of the benefits of measuring analytes in biological samples.Advancements in the medical sciences are identifying a growing number ofanalytes that can be electrochemically analyzed by, for example,determining analyte concentrations in a fluidic sample.

The accuracy of current methods of electrochemically measuring analytessuch as glucose can be negatively affected by a number of confoundingvariables including variations in reagent thickness, wetting of thereagent, rate of sample diffusion, hematocrit (Hct), temperature, saltand other confounding variables. These confounding variables can causean increase or decrease in an observed magnitude of, for example, acurrent that is proportional to glucose, thereby causing a deviationfrom the “true” glucose concentration.

Current methods and systems provide some advantages with respect toconvenience; however, there remains a need for new methods ofelectrochemically measuring an analyte in a fluid sample even in thepresence of confounding variables.

BRIEF SUMMARY

In view of the disadvantages noted above, the disclosure describesmethods of electrochemically measuring an analyte in a fluidic samplesuch as a body fluid. The methods are based upon an inventive conceptthat includes building within- and across-pulse descriptors derived frominformation obtained from an electrical test sequence having at leastone DC block, where the at least one DC block includes a sequence of atleast one excitation potential and at least one recovery potential undera closed circuit. For example, information such as current response,shape and/or magnitude of the excitation pulses and/or recovery pulsescan be used to determine the effects of Hct, salt concentration and/ortemperature on the analyte concentration. This information can be builtinto descriptors for use in algorithms for determining an analyteconcentration such as a glucose concentration. The inventive concepttherefore provides certain advantages, effects, features and objectswhen compared to known methods of measuring an analyte concentration (orvalue) in a fluidic sample.

In one aspect, an electrochemical analysis method is provided formeasuring, determining, calculating or otherwise predicting an analyteconcentration in a fluidic sample that has been applied to anelectrochemical biosensor. The method can include at least a step ofproviding a test sequence of at least one DC block to the fluidicsample, where the test block is designed to elicit specific informationabout Hct, salt concentration and/or temperature effects, where the DCblock includes at least one excitation potential and at least onerecovery potential, and where a closed circuit condition of an electrodesystem of the biosensor is maintained during the DC block. The methodalso can include a step of measuring response information to the testsequence or obtaining response information therefrom.

In some instances, the at least one DC block is pulsed as a continuous,unipolar excitation waveform (i.e., the potential is applied andcontrolled throughout the DC block in a closed circuit), which is incontrast to some pulsed amperometric methods that employ an open circuitbetween excitation pulses. The DC block includes a plurality ofshort-duration excitation pulses and recovery pulses optimized fordetecting an analyte such as glucose, the optimization pertaining topulse duration, ramped transitions between the excitation pulse andrecovery pulse, number of current responses measured during each pulse,and where in each pulse current response measurements are taken. The DCblock can be from at least one (1) pulse to about ten (10) pulses at apotential that alternates between about 0 mV to about +450 mV in aclosed circuit. Each of the DC pulses can be applied for about 50 msecto about 500 msec. Moreover, the ramp rate can be from about 10 mV/msecto about 50 mV/msec.

In some instances, the test sequence also can include at least one ACblock. In other instances, the test sequence also can include a secondDC block. In still other instances, the test sequence includes both theat least one AC block and the second DC block.

In addition, the method can include a step of building at least onewithin-pulse descriptor and/or at least one across-pulse descriptor thatis based upon response currents to the excitation and/or recoverypotentials of the DC block to correct and/or compensate for Hct, saltconcentration and/or temperature effects on the analyte concentration.The descriptors encode magnitude and shape information of currentresponses to the test sequence.

Advantageously, by using and applying the descriptors, analyteconcentration varies only by ±10% or less for sample Hct varying fromabout 20% to about 70%, sample salt varying from about 140 mg/dL toabout 180 mg/dL, and/or sample temperatures varying from about 6° C. toabout 44° C.

In view of the foregoing, devices, apparatuses and systems used inconnection with electrochemical analysis are provided that incorporateone or more of the descriptor-based measurement methods disclosedherein. These devices, apparatuses and systems can be used to determineconcentration of analytes including, but not limited to, amino acids,antibodies, bacteria, carbohydrates, drugs, lipids, markers, nucleicacids, peptides, proteins, toxins, viruses and other analytes, as wellas combinations thereof. In certain instances, the analyte is glucose.

These and other advantages, effects, features and objects of theinventive concept will become better understood from the descriptionthat follows. In the description, reference is made to the accompanyingdrawings, which form a part hereof and in which there is shown by way ofillustration, not limitation, embodiments of the inventive concept.

BRIEF DESCRIPTION OF THE DRAWINGS

The advantages, effects, features and objects other than those set forthabove will become more readily apparent when consideration is given tothe detailed description below. Such detailed description makesreference to the following drawings, wherein:

FIG. 1 shows an exemplary analyte test system comprising a meter and abiosensor.

FIG. 2 shows a simplified circuit diagram for an exemplary analytemeasurement system.

FIG. 3 is a graph of an exemplary test sequence of an analytemeasurement system.

FIG. 4 is a graph of an exemplary response of an analyte measurementsystem to the test sequence of FIG. 3.

FIG. 5 is an enlarged view illustrating portions of the test sequence ofFIG. 3 and the response of FIG. 4.

FIG. 6 is a graph illustrating current responses for test samples withvarying Hct concentrations, constant temperatures, and constant glucoseconcentrations.

FIG. 7 is a graph illustrating current responses for test samples withvarying temperatures, constant Hct concentrations and constant glucoseconcentrations.

FIG. 8 is a graph illustrating recovery current response information fortest samples with varying temperatures and varying Hct concentrations.

FIG. 9 is a graph illustrating excitation current response informationfor test samples with varying temperatures and varying Hctconcentrations.

FIG. 10 is a flow diagram illustrating an exemplary method.

While the inventive concept is susceptible to various modifications andalternative forms, exemplary embodiments thereof are shown by way ofexample in the drawings and are herein described in detail. It should beunderstood, however, that the description of exemplary embodiments thatfollows is not intended to limit the inventive concept to the particularforms disclosed, but on the contrary, the intention is to cover alladvantages, effects, features and objects falling within the spirit andscope thereof as defined by the embodiments above and the claims below.Reference should therefore be made to the embodiments above and claimsbelow for interpreting the scope of the inventive concept. As such, itshould be noted that the embodiments described herein may haveadvantages, effects, features and objects useful in solving otherproblems.

DESCRIPTION OF PREFERRED EMBODIMENTS

The methods, devices, apparatuses and systems now will be described morefully hereinafter with reference to the accompanying drawings, in whichsome, but not all embodiments of the inventive concept are shown.Indeed, the methods, devices, apparatuses and systems may be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will satisfy applicable legal requirements.

Likewise, many modifications and other embodiments of the methods,devices, apparatuses and systems described herein will come to mind toone of skill in the art to which the disclosure pertains having thebenefit of the teachings presented in the foregoing descriptions and theassociated drawings. Therefore, it is to be understood that the methods,devices, apparatuses and systems are not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended claims.Although specific terms are employed herein, they are used in a genericand descriptive sense only and not for purposes of limitation.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of skill in the artto which the disclosure pertains. Although any methods and materialssimilar to or equivalent to those described herein can be used in thepractice or testing of the methods, devices, apparatuses and systems,the preferred methods and materials are described herein.

Moreover, reference to an element by the indefinite article “a” or “an”does not exclude the possibility that more than one element is present,unless the context clearly requires that there be one and only oneelement. The indefinite article “a” or “an” thus usually means “at leastone.”

Overview

Analyte measurement methods are disclosed herein that use informationderived from DC current responses to provide an analyte concentration ina reliable manner. These measurement methods also can be used to reducethe effects of confounding variables such as Hct, salt concentration,temperature and/or variations in reagent thickness, thereby providing amore “true” analyte concentration.

The measurement methods disclosed herein largely utilize amperometry;however, it is contemplated that the methods can be used with otherelectrochemical measurement methods (e.g., coulometry, potentiomerty orvoltammetry). Additional details regarding exemplary electrochemicalmeasurement methods are disclosed in, for example, U.S. Pat. Nos.4,008,448; 4,225,410; 4,233,029; 4,323,536; 4,891,319; 4,919,770;4,963,814; 4,999,582; 4,999,632; 5,053,199; 5,108,564; 5,120,420;5,122,244; 5,128,015; 5,243,516; 5,288,636; 5,352,351; 5,366,609;5,385,846; 5,405,511; 5,413,690; 5,437,999; 5,438,271; 5,508,171;5,526,111; 5,627,075; 5,628,890; 5,682,884; 5,727,548; 5,762,770;5,858,691; 5,997,817; 6,004,441; 6,054,039; 6,254,736; 6,270,637;6,645,368; 6,662,439; 7,073,246; 7,018,843; 7,018,848; 7,045,054;7,115,362; 7,276,146; 7,276,147; 7,335,286; 7,338,639; 7,386,937;7,390,667; 7,407,811; 7,429,865; 7,452,457; 7,488,601; 7,494,816;7,545,148; 7,556,723; 7,569,126; 7,597,793; 7,638,033; 7,731,835;7,751,864; 7,977,112; 7,981,363; 8,148,164; 8,298,828; 8,329,026;8,377,707; and 8,420,404, as well as RE36268, RE42560, RE42924 andRE42953.

Advantageously, the methods described herein can be incorporated intoSMBG devices, apparatuses and systems to more accurately and quicklyreport an analyte concentration, such as a glucose concentration,especially a blood glucose concentration.

Moreover, the measurement methods can be implemented using advancedmicroprocessor-based algorithms and processes that result indramatically improved system performance. These measurement methods alsooffer flexibility and number of ways to create algorithms that canachieve improved performance such as 10/10 performance. As used herein,“10/10 performance” means that a measured bG value is within about ±10%of the actual bG value for bG concentrations >100 mg/dL, and within ±10mg/dL of the actual bG value for bG concentrations <100 mg/dL.

Details regarding additional electrochemical measurement methods thatmay be useful in performing the methods disclosed herein can be found inthe following co-filed and co-pending patent applications titled:“METHODS OF SCALING DATA USED TO CONSTRUCT BIOSENSOR ALGORITHMS AS WELLAS DEVICES, APPARATUSES AND SYSTEMS INCORPORATING THE SAME” (Int'lPatent Application No. PCT/EP2014/054952); “METHODS OF ELECTROCHEMICALLYMEASURING AN ANALYTE WITH A TEST SEQUENCE HAVING A PULSED DC BLOCK ASWELL AS DEVICES, APPARATUSES AND SYSTEMS INCORPORATING THE SAME” (Int'lPatent Application No. PCT/EP2014/054965); “METHODS OF FAILSAFINGELECTROCHEMICAL MEASUREMENTS OF AN ANALYTE AS WELL AS DEVICES,APPARATUSES AND SYSTEMS INCORPORATING THE SAME” (Int'l PatentApplication No. PCT/EP2014/054955); “METHODS OF USING INFORMATION FROMRECOVERY PULSES IN ELECTROCHEMICAL ANALYTE MEASUREMENTS AS WELL ASDEVICES, APPARATUSES AND SYSTEMS INCORPORATING THE SAME” (Int'l PatentApplication No. PCT/EP2014/054943); and “METHODS OF DETECTING HIGHANTIOXIDANT LEVELS DURING ELECTROCHEMICAL MEASUREMENTS AND FAILSAFING ANANALYTE CONCENTRATION THEREFROM AS WELL AS DEVICES, APPARATUSES ANDSYSTEMS INCORPORATING THE SAME” (Int'l Patent Application No.PCT/EP2014/054962).

Analyte Measurement Devices, Apparatuses and Systems

Prior to, and in connection with, describing the inventive measurementmethods, FIG. 1 shows an exemplary analyte measurement system includinga device such as a test meter 11 operatively coupled with anelectrochemical biosensor 20 (also known as a test element). Meter 11and biosensor 20 are operable to determine concentration of one or moreanalytes in a fluidic sample provided to the biosensor 20. In someinstances, the sample may be a body fluid sample such as, for example,whole blood, plasma, serum, urine or saliva. In other instances, thefluidic sample may be another type of sample to be tested for thepresence or concentration of one or more electrochemically reactiveanalyte(s) such as an aqueous environmental sample.

In FIG. 1, the biosensor 20 is a single use test strip removablyinserted into a connection terminal 14 of meter 11. In some instances,biosensor 20 is configured as a blood glucose test element and includesfeatures and functionalities for electrochemically measuring glucose. Inother instances, biosensor 20 is configured to electrochemically measureone or more other analytes such as, for example, amino acids,antibodies, bacteria, carbohydrates, drugs, lipids, markers, nucleicacids, peptides, proteins, toxins, viruses, and other analytes.

Meter 11 includes an electronic display 16 that is used to displayvarious types of information to the user including analyteconcentration(s) or other test results, and user interface 50 forreceiving user input. Meter 11 further includes a microcontroller andassociated test signal generating and measuring circuitry (not shown)that are operable to generate a test signal, to apply the signal to thebiosensor 20, and to measure one or more responses of the biosensor 20to the test signal. In some instances, meter 11 can be configured as ablood glucose measurement meter and includes features andfunctionalities of the ACCU-CHEK® AVIVA® meter as described in thebooklet “Accu-Chek® Aviva Blood Glucose Meter Owner's Booklet” (2007),portions of which are disclosed in U.S. Pat. No. 6,645,368. In otherinstances, meter 11 can be configured to electrochemically measure oneor more other analytes such as, for example, amino acids, antibodies,bacteria, carbohydrates, drugs, lipids, markers, nucleic acids,proteins, peptides, toxins, viruses, and other analytes. Additionaldetails regarding exemplary meters configured for use withelectrochemical measurement methods are disclosed in, for example, U.S.Pat. Nos. 4,720,372; 4,963,814; 4,999,582; 4,999,632; 5,243,516;5,282,950; 5,366,609; 5,371,687; 5,379,214; 5,405,511; 5,438,271;5,594,906; 6,134,504; 6,144,922; 6,413,213; 6,425,863; 6,635,167;6,645,368; 6,787,109; 6,927,749; 6,945,955; 7,208,119; 7,291,107;7,347,973; 7,569,126; 7,601,299; 7,638,095 and 8,431,408.

One of skill in the art understands that the measurement methodsdescribed herein can be used in other measurement, devices, apparatuses,systems and environments such as, for example, hospital test systems,laboratory test systems and others.

It shall be understood that the meter and biosensor can includeadditional and/or alternate attributes and features in addition to orinstead of those shown in FIG. 1. For example, the biosensor can be inthe form of a single use, disposable electrochemical test strip having asubstantially rectangular shape. It shall be appreciated that thebiosensors can include different forms such as, for example, test stripsof different configurations, dimensions or shapes, non-strip testelements, disposable test elements, reusable test elements,micro-arrays, lab-on-chip devices, bio-chips, bio-discs, bio-cds orother test elements. Additional details regarding exemplary biosensorsconfigured for use with electrochemical measurement methods aredisclosed in, for example, U.S. Pat. Nos. 5,694,932; 5,762,770;5,948,695; 5,975,153; 5,997,817; 6,001,239; 6,025,203; 6,162,639;6,245,215; 6,271,045; 6,319,719; 6,406,672; 6,413,395; 6,428,664;6,447,657; 6,451,264; 6,455,324; 6,488,828; 6,506,575; 6,540,890;6,562,210; 6,582,573; 6,592,815; 6,627,057; 6,638,772; 6,755,949;6,767,440; 6,780,296; 6,780,651; 6,814,843; 6,814,844; 6,858,433;6,866,758; 7,008,799; 7,063,774; 7,238,534; 7,473,398; 7,476,827;7,479,211; 7,510,643; 7,727,467; 7,780,827; 7,820,451; 7,867,369;7,892,849; 8,180,423; 8,298,401; 8,329,026, as well as RE42560, RE42924and RE42953.

FIG. 2 shows a simplified circuit diagram 400 of an exemplary analytemeasurement system including a biosensor 420 operatively coupled with ameter 410 to provide electrical communication between biosensor 420 andmeter 410. Biosensor 420 includes a test cell 421 having a workingelectrode 422 and a counter electrode 423 in contact with a combinedreagent and sample 422. Working electrode 422 is in electricalcommunication with the negative input of amplifier 414 of meter 410.Counter electrode 423 is in electrical communication with a virtualground or reference potential of meter 410.

Meter 410 includes a microcontroller 411, which is operable to generateand output a test control signal at output 412. The test control signaldrives amplifier 413 to output a test potential to the positive input ofamplifier 414. This test potential also is seen at the negative input ofamplifier 414 due to a virtual short between the positive input andnegative input of amplifier 414. The test potential present at thenegative input of amplifier 414 provided to working electrode 422. Thus,the test control signal output by microcontroller 411 is operable tocontrol the test potential applied to the working electrode 422. Thetest control signal provided at output 412 and test potential providedto working electrode 422 may include a number features such as ACcomponents, preconditioning components, and DC pulse sequences includingexcitation potentials and closed circuit recovery potentials, examplesof which are further described herein below.

The test potential applied to working electrode 422 produces a currentresponse 450 that is provided to the negative input of amplifier 414.Amplifier 414 is configured as an IN converter and outputs a voltage toinput 460 of microcontroller 411 that is proportional to currentresponse 450. Microcontroller 411 detects the voltage at input 460 anddetermines the current response 450 by dividing the voltage seen atinput 460 by the value of gain resistor 415. The current response 450may include responses to test potentials including AC components,preconditioning components, and DC pulse sequences including excitationpotentials and closed circuit recovery potentials, examples of which arefurther described herein below.

It shall be appreciated that additional exemplary analyte measurementsystems may include a number of features in addition to or asalternatives to those illustrated in simplified circuit diagram 400. Forexample, microcontroller 411 also may be operatively connected to othercomponents of meter 410 such as one or more digital memories, displaysand/or user interfaces, such as those illustrated and described above inconnection with FIG. 1, as well as controller and driver circuitryassociated therewith. In FIG. 2, output 412 is an analog outputconnected to a D/A converter internal to microcontroller 412, and input460 is an analog input connected to an A/D converter internal tomicrocontroller 412. In other instances, output 412 may be a digitaloutput connected to an external D/A converter and input 460 may be adigital input connected to an external A/D converter. In FIG. 2, testcell 421 is a two-electrode test cell; however, other test cells can bethree-electrode test cells, or other electrode systems.

In FIG. 2, a test potential can be applied to a working electrode toprovide a potential difference between the working electrode and acounter electrode. Alternatively, a test potential other than virtualground or reference potential can be provided as a counter electrode toprovide a potential difference between the working electrode and acounter electrode. It shall be appreciated that the foregoing and avariety of other additional and alternate test cell, electrode, and/orcircuitry configurations operable to apply a test signal to an electrodesystem in contact with a combined sample and reagent and measure aresponse thereto may be utilized.

Measurement Methods

As noted above, the measurement methods described herein are based uponan inventive concept that includes using information derived from DCresponses to a test sequence having at least one DC block, where theblock is designed to provide specific information about aspects of asample and/or biosensor.

The methods generally include applying to a fluidic sample, such as abody fluid, an AC block in connection with a pulsed DC sequence andmeasuring the AC and DC current responses. As shown in FIGS. 3-4, onetrace illustrates the applied DC potential, and the other traceillustrates the AC and DC current responses, respectively. The appliedDC potential can be fixed at about 0 mV between pulses to provide arecovery pulse, thus making it a generally continuous, unipolarexcitation waveform. This is in contrast to a test sequence from knownmethods that prescribe the use of an open circuit between positive DCpulses, thereby excluding the possibility of collecting and analyzingthe current between positive pulses.

As used herein, “recovery pulse” means an about zero-potential pulseapplied for an adequately long recovery period in which theelectrochemical reaction with the analyte of interested (e.g., glucose)is turned “off,” thereby allowing the system to return to a fixedstarting point before subsequent interrogation with another morepositive DC pulse.

The test sequence thus generally includes a block of low-amplitude ACsignals followed by a controlled, DC block.

With respect to the AC block, it can include a plurality of AC segmentssuch as, for example, from about 2 segments to about 10 segments, fromabout 3 segments to about 9 segments, from about 4 segments to about 8segments, from about 5 segments to about 7 segments, or about 6segments. In other instances, the AC block can include about 2 segments,about 3 segments, about 4 segments, about 5 segments, about 6 segments,about 7 segments, about 8 segments, about 9 segments, or about 10segments. In still other instances, the AC block can have more than 10segments, that is, about 15 segments, about 20 segments, or about 25segments. In yet other instances, the AC block can include 1 segment,where the segment has multiple low-amplitude AC signals appliedsimultaneously.

One of skill in the art understands that the number of AC segments willbe limited by the complexity of the response, the associated frequencyrange and time available to perform the measurements. Higher frequenciesgenerally require high bandwidth electronics and faster sampling,whereas lower frequencies take longer and typically are noisier. Themaximum number of segments therefore will be a compromise of theseparameters, choosing the minimum count and frequency span needed todiscriminate the sample and environmental and/or confounding factors ofinterest.

As used herein, “about” means within a statistically meaningful range ofa value or values such as a stated concentration, length, molecularweight, pH, potential, time frame, temperature, voltage or volume. Sucha value or range can be within an order of magnitude, typically within20%, more typically within 10%, and even more typically within 5% of agiven value or range. The allowable variation encompassed by “about”will depend upon the particular system under study, and can be readilyappreciated by one of skill in the art.

The frequency of each signal in each segment of the AC block can be fromabout 1 kHz to about 20 kHz, from about 2 kHz to about 19 kHz, fromabout 3 kHz to about 18 kHz, from about 4 kHz to about 17 kHz, fromabout 5 kHz to about 16 kHz, from about 6 kHz to about 15 kHz, fromabout 7 kHz to about 14 kHz, from about 8 kHz to about 13 kHz, fromabout 9 kHz to about 12 kHz or from about 10 kHz to about 11 kHz. Inother instances, the frequency of each segment in the AC block can beabout 1 kHz, about 2 kHz, about 3 kHz, about 4 kHz, about 5 kHz, about 6kHz, about 7 kHz, about 8 kHz, about 9 kHz, about 10 kHz, about 11 kHz,about 12 kHz, about 13 kHz, about 14 kHz, about 15 kHz, about 16 kHz,about 17 kHz, about 18 kHz, about 19 kHz, or about 20 kHz. In stillother instances, the frequency of each signal in each segment of the ACblock can be more than 20 kHz, that is, about 30 kHz, about 40 kHz, orabout 50 kHz. In some instances, one or more of the segments can havethe same frequency, whereas in other instances each segment has adistinct frequency from the other segments. Four frequencies, however,generally is adequate. The exact frequencies employed can be readilygenerated by simple integer division of a measurement system clock'smaximum frequency.

A maximum frequency limit for a signal in a segment of the AC block,however, can be up to about 100 kHz for an inexpensive, battery-poweredhandheld instrument. Beyond that, the increasing demands on analogbandwidth, sampling rate, storage and processing speed quickly add up,while the imaginary portion of a typical biosensor response becomesincreasingly smaller with frequency. Lower frequencies have longerperiods and take longer times to sample with comparable accuracy.

The AC block typically includes at least two different low-amplitudesignals. For example, the AC block can include two (2) segments at two(2) frequencies such as, for example, about 10 kHz or about 20 kHzfollowed by about 1 kHz or about 2 kHz. In other instances, the AC blockincludes a plurality of low-amplitude signals. For example, the AC blockcan have five (5) segments at four (4) frequencies such as, for example,about 10 kHz, about 20 kHz, about 10 kHz, about 2 kHz and about 1 kHz.Alternatively, the AC block can have four (4) segments at four (4)frequencies such as, for example, about 20 kHz, about 10 kHz, about 2kHz and about 1 kHz. Alternatively, the AC block can have four (4)frequencies applied simultaneously at about 10 kHz, about 20 kHz, about10 kHz, about 2 kHz and about 1 kHz. Alternately still, the AC block canhave a multi-frequency excitation waveform that simultaneously appliesthe desired low-amplitude AC signals. The AC frequencies may be appliedsequentially, or combined and applied simultaneously and analyzed viaFourier Transform.

The AC block can be applied for about 500 msec to about 1.5 sec, about600 msec to about 1.25 sec, about 700 msec to about 1000 msec, or about800 msec to about 900 msec. Alternatively, the AC block can be appliedfor about 500 msec, about 600 msec, about 700 msec, about 800 msec,about 900 msec, about 1000 msec, about 1.25 sec or about 1.5 sec. Inparticular, the AC block can be applied for about 100 msec to about 300msec.

One of skill in the art, however, understands that the number,frequency, duration and order of the AC segments can be varied.

AC current response information can be obtained at any time during atest sequence. Impedance results at lower frequencies may be influencedby analyte concentration if obtained after an electrochemical cell is DCpolarized. In some instances, a series of AC current responsemeasurements can be obtained early in the test sequence. Measurementstaken shortly after a fluidic sample is applied to a biosensor will beinfluenced by diffusion, temperature and reagent solubility. In otherinstances, the AC response current measurements can be obtained at asufficient time after an adequate sample has been applied to allow theresponse to stabilize, and avoid the transient response in the firstsecond. Likewise, response current measurements can be made at one ormore frequencies. Due to their capacitive nature, multiple ACmeasurements separated by a frequency octave or decade may offerdifferent sensitivities or easier manipulation.

Additional details regarding exemplary AC blocks in electrochemicalmeasurement methods are disclosed in, for example, U.S. Pat. Nos.7,338,639; 7,390,667; 7,407,811; 7,417,811; 7,452,457; 7,488,601;7,494,816; 7,597,793; 7,638,033; 7,751,864; 7,977,112; 7,981,363;8,148,164; 8,298,828; 8,377,707 and 8,420,404.

With respect to the DC block, it can include a plurality of pulses suchas, for example, from about 2 pulses to about 10 pulses, from about 3pulses to about 9 pulses, from about 4 pulses to about 8 pulses, fromabout 5 pulses to about 7 pulses, or about 6 pulses. In other instances,the DC block can include about 2 pulses, about 3 pulses, about 4 pulses,about 5 pulses, about 6 pulses, about 7 pulses, about 8 pulses, about 9pulses, or about 10 pulses. In still other instances, the DC block canhave more than 10 pulses, that is, about 15 pulses, about 20 pulses, orabout 25 pulses. As used herein, “pulse” means at least one excitationand one recovery period.

The DC block typically includes a constantly applied potentialdifference that alternates between about 0 mV and about +450 mVpotential difference, or other slowly time-varying potential differencethat can be analyzed by traditional DC electrochemical methods. One ofskill in the art, however, understands that the range for the appliedpotential difference can, and will, vary depending upon the analyte andreagent chemistry used. As such, excitation pulse potential can begreater-than, less-than or equal to about +450 mV. Examples ofexcitation potentials include, but are not limited to, 50 mV, 75 mV, 100mV, 125 mV, 150 mV, 175 mV, 200 mV, 225 mV, 250 mV, 275 mV, 300 mV, 325mV, 350 mV, 375 mV, 400 mV, 425 mV, 450 mV, 475 mV, 500 mV, 525 mV, 550mV, 575 mV, 600 mV, 625 mV, 650 mV, 675 mV, 700 mV, 725 mV. 750 mV, 775mV, 800 mV, 825 mV, 850 mV, 875 mV, 900 mV, 925 mV, 950 mV, 975 mV or1000 mV.

Regardless of the number, each DC pulse can be applied for about 50 msecto about 500 msec, about 60 msec to about 450 msec, about 70 msec toabout 400 msec, about 80 msec to about 350 msec, about 90 msec to about300 msec, about 100 msec to about 250 msec, about 150 msec to about 200msec, or about 175 msec. Alternatively, each pulse can be applied forabout 50 msec, about 60 msec, about 70 msec, about 80 msec, about 90msec, about 100 msec, about 125 msec, about 150 msec, about 175 msec,about 200 msec, about 225 msec, about 250 msec, about 275 msec, about300 msec, about 325 msec, about 350 msec, about 375 msec, about 400msec, about 425 msec, about 450 msec, about 475 msec or about 500 msec.In particular, each DC pulse at +450 mV can be applied for about 250msec, and each DC pulse at 0 mV can be applied for about 500 msec.Alternatively still, each pulse can be applied for less than about 50msec or more than about 500 msec.

Generally, the ramp rate of each DC pulse is selected to provide about50% or greater reduction in peak current relative to the peak currentprovided by a nearly ideal potential transition. In some instances, eachpulse can have the same ramp rate. In other instances, some pulses canhave the same ramp rate and other pulses can have a different ramp rate.In still other instances, each pulse has its own ramp rate. For example,effective ramp rates can be from about 5 mV/msec to about 75 mV/msec orfrom about 10 mV/msec to about 50 mV/msec, 15 mV/msec to about 25mV/msec, or about 20 mV/msec. Alternatively, the ramp rate can be about5 mV/msec, about 10 mV/msec, about 15 mV/msec, about 20 mV/msec, about25 mV/msec, about 30 mV/msec, about 35 mV/msec, about 40 mV/msec, about45 mV/msec, about 50 mV/msec, about 55 mV/msec, about 60 mV/msec, about65 mV/msec, about 70 mV/msec, or about 75 mV/msec. In particular, theramp rate can be from about 40 mV/msec to about 50 mV/msec.

Like the AC block, one of skill in the art understands that the number,potential, duration and order of the DC pulses can be varied.

AC and/or DC current response information is collected from the testsequence and includes current responses to the AC and DC blocks. In someinstances, the current response information can be collected at an A/Dsampling rate for DC and AC measurements to simplify the system design,including a single shared signal path for AC and DC measurements. Commondigital audio sampling rates range include, but are not limited to, fromabout 44.1 kHz to about 192 kHz. A/D converters in this range arereadily available from variety of commercial semiconductor suppliers.

As part of the inventive concept, it has been recognized that therecovery responses include unique informational content, particularlypertaining to Hct, salt concentration and temperature. Furthermore, thisinformation provides value and can be used to further refine accuracyand performance of SMBG devices, apparatuses and systems.

Returning to FIG. 3, the responses to the pulsed DC block encode Hct andtemperature information, as well as real-time information about otherimportant processes, such as wetting of the reagent, sample diffusionand separation with respect to the reagent, the establishment of astable glucose transport gradient, and the kinetics associated with thereducible analyte. The illustrated DC block provides short, distinctstrobing of these processes with respect to time. Each positive DC pulseproduces a distinct current signature, which is not exactly like theothers due to its position in time.

Importantly, each closed circuit recovery potential pulse provides anadequately long recovery period in which the electrochemical reactionwith glucose is turned off, thereby allowing the system to return to acommon starting point before subsequent interrogation with anotherpositive pulse.

Just as the shapes of the current decays from positive DC pulses encodeinformation about glucose, Hct and temperature (as well as the otherbiosensor processes noted above), the shapes of the recovery pulses alsoare unique. Each recovery pulse produces a negative current responsewith a rate of growth that also encodes distinct, time-orderedinformation describing how the biamperometric system returns to a givenreference state. The rate of current growth during the recovery pulse isnot simply a mirror image of the current decay associated with aneighboring positive DC pulse, because the glucose reaction has beenturned off by selecting a potential magnitude that cannot initiate andsustain the electrochemical reaction with glucose. The exemplary methodsdisclosed herein utilize unique information content pertaining to Hct,temperature and other confounding variables encoded by differenceswithin and across the excitation and/or recovery current responses toimprove the accuracy and performance SMBG devices, apparatuses andsystems.

It shall be appreciated that near-zero, and non-zero positive andnegative potential magnitudes also may be utilized as recovery pulses inadditional embodiments, and that the magnitude, duration, and shapes ofall pulses may vary from the illustrated exemplary embodiments. It alsoshall be appreciated that the exemplary embodiments disclosed herein donot restrict the number of AC frequencies that may be employed, theirpositions in time, or their amplitude(s)/frequencies. Nor does itrestrict interspersing AC frequencies within the DC block of the testsequence, such as in the exemplary test s illustrated in FIG. 3 anddiscussed in greater detail below. Furthermore, the exemplaryembodiments disclosed herein do not restrict the number, length ormagnitude of the DC pulses.

FIG. 3 shows an exemplary test sequence 500 that can be provided to anelectrode system of an electrochemical test cell. The vertical axis 501of graph denotes working electrode potential in volts (V). It shall beunderstood that working electrode potential may refer to a potentialapplied to a working electrode or to a potential difference between aworking electrode and another electrode such as a counter or referenceelectrode regardless of the electrode or electrodes to which a potentialor a test signal is applied. The horizontal axis 502 of graph denotestime in sec. Test sequence 500 is applied at or after time=0 sec, whichis a time at which a sufficient sample is present in a test cell as maybe determined using sample sufficiency detection electrodes and signalsor through other techniques.

Test sequence 500 begins with a signal component 510 (or block) that mayinclude one or more AC segment(s), preconditioning test segment(s) orcombinations thereof. Signal component 510 also may include incubationsignal components that are selected not to drive an electrochemicalreaction but to allow for reagent hydration and progression of reactionkinetics. Such incubation components may include, for example, an opencircuit condition, a 0 mV potential, a substantially 0 mV averagepotential, or a non-zero volt potential such as a non-zero potentialthat is less than the potential needed to drive a particular reaction ofinterest.

In some instances, signal component 510 comprises one or more ACsegments and frequencies provided to an electrode system of anelectrochemical test cell. For example, the AC segments of signalcomponent 510 include a 10 kHz segment applied from about time=0 sec toabout time=1.2 sec, a 20 kHz segment applied from about time=1.2 sec toabout time=1.3 sec, a 10 kHz segment applied from about time=1.3 sec toabout time=1.4 sec, a 2 kHz segment applied from about time=1.4 sec toabout time=1.5 sec, and a 1 kHz segment applied from about time=1.5 secto about time=1.6 sec. Alternatively, the AC segments and frequencies ofsignal component 510 includes a 10 kHz signal applied for about 1.5 sec,followed by a 20 kHz signal applied for about 0.2 sec, followed by a 10kHz signal applied for about 0.2 sec, followed by a 2 kHz signal appliedfor about 0.2 sec, followed by a 1 kHz signal applied for about 0.2 sec.

As noted above, the signal component 510 can include one or morepreconditioning signal(s). In some instances, the signal component 510includes a positive DC preconditioning pulse applied starting at abouttime=0 sec for about 200-600 msec and having an amplitude of about 100mV or greater. In other instances, the signal component 510 includes apositive DC preconditioning pulse applied starting at about time=0 secfor about 500 msec and having an amplitude of about 450 mV. In stillother instances, the signal component 510 includes a two cycletriangular potential wave including a slew rate of about 2 V/s.

As such, the signal component 510 can include combinations of one ormore AC segments as well as preconditioning signal component(s). In someinstances, the signal component 510 includes one or more AC signalcomponents followed by one or more preconditioning signal components. Inother instances, the signal component 510 includes one or morepreconditioning signal components followed by one or more AC signalcomponents.

After signal component 510, a pulsed DC sequence 520 (or block) isapplied to the electrode system. Pulse sequence 520 begins with theworking electrode potential being ramped up to the excitation potentialof pulse 521. From pulse 521 the working electrode potential is rampeddown to the recovery potential of pulse 522. From potential 522 theworking electrode potential is sequentially ramped up and down to thepotentials of pulses 523-532. As shown in FIG. 3, the ramping betweenpulses is controlled to occur at a predetermined rate effective tomitigate capacitive current response. In some instances, the ramp rateis selected to provide a 50% or greater reduction in peak currentrelative to the peak current provided by a substantially square waveexcitation in which signal rise time is determined by the nativecharacteristics of the driving circuitry rather than being deliberatelycontrolled according to a predetermined target rate or range.

Pulses 521, 523, 525, 527, 529 and 531 are examples of ramp-ratecontrolled excitation potential pulses that provide an excitationpotential to an electrochemical test cell effective to drive anelectrochemical reaction in the test cell and generate an associatedFaradaic current response which may be convolved with capacitivecharging current responses and other current response informationattributable to a plurality of confounding variables. As also shown inFIG. 3, the excitation potential pulses provide a potential differencebetween a working electrode and a counter electrode of about 450 mV thatis about 130 msec in duration. The excitation potential shown isselected to drive a particular analyte reaction, which in this case isan enzyme-mediated reaction of glucose. It shall be understood that themagnitude and duration of the excitation potential pulses may varydepending upon the particular activation potential of the mediator usedor the potential needed to drive a particular reaction of interest.

Pulses 522, 524, 526, 528, 530 and 532 are examples of closed circuitrecovery potential pulses that provide a potential to a workingelectrode of an electrochemical test cell during which a closed circuitcondition of the test cell is maintained to control the test cell todischarge current and to more rapidly restore test cell conditions to asubstantially common starting point for subsequent interrogation with anexcitation potential pulse. Closed circuit recovery potential pulsesalso may be ramp rate controlled in the same or a similar manner toexcitation potential pulses. As shown in FIG. 3, the recovery potentialpulses provide a potential difference between a working electrode and acounter electrode of about 0 mV, which is about 280 msec in durationduring which the electrode system is maintained in a closed circuitcondition.

In some instances, the magnitude of the DC potential provided by aclosed circuit recovery pulse and its duration may vary depending uponthe potential below which a test cell can recover toward apre-excitation state and the time needed to provide a desired response.Thus, some embodiments can include recovery potential pulses having anon-zero potential that is less than the activation potential of a givenmediator. Some instances include recovery potential pulses having anon-zero potential that is less than the potential needed to drive aparticular reaction of interest. Other instances include recoverypotential pulses having a non-zero potential that is less than theminimum redox potential for a specified reagent system. Still otherinstances include recovery potential pulses having an average potentialof about 0 mV, but which have pulse portions greater than 0 mV andportions less than 0 mV. Still other instances include recoverypotential pulses having an average potential according to any of theaforementioned non-zero potentials, but which have portions greater thanthe non-zero average and portions less than the non-zero average.

FIG. 4 shows a current response 600 produced by a test cell in responseto test sequence 500 of FIG. 3. The vertical axis 601 of graph 600denotes working electrode current in μA. The horizontal axis 602 ofgraph 600 denotes time in seconds. Current response 600 begins withresponse component 610 that includes a response to signal component 510.In some instances, response component 610 includes AC current responsesfrom which impedance, admittance and phase angle can be determined. Suchmeasurements may be performed for one or more AC block segments orcomponents such as those described above in connection with FIG. 3. Insome instances, response component 610 includes a preconditioning signalcomponent but no AC segment and no measurement of response component 610is performed. In other instances, response component 610 includes acombination of the foregoing and/or other components.

After response component 610, response 600 includes a sequence ofexponentially decaying excitation current responses 621, 623, 625, 627,629 and 631, which are generated in response to excitation pulses 521,523, 525, 527, 529 and 531, respectively. Excitation current responses621, 623, 625, 627, 629 and 631 include a Faradaic current responsecomponent relating to an electrochemical reaction in the test cell aswell as a capacitive charging current response relating to capacitiveelectrode charging and current response information attributable to aplurality of confounding variables. Current responses 622, 624, 626,628, 630 and 632 include a recovery current response relating todischarge of the test cell when maintained in a closed circuit conditionapplying a recovery potential and current response informationattributable to a plurality of confounding variables.

Current responses 621-632 include information related to theconcentration of an analyte of interest that may be present in thefluidic sample being tested, as well as additional information ofconfounding variables convolved therewith. This inventive conceptdescribed herein therefore can be incorporated into methods by which theinformation associated with current responses 621-631 can be used todetermine a concentration of an analyte of interest with enhancedaccuracy, precision, repeatability and reliability by compensating foror decreasing sensitivity to one or more confounding variables. A numberof confounding variables may impact analyte concentration determinationsincluding variations in reagent film thickness, sample temperature,sample Hct, reagent wetting, and reaction kinetics among others. Thepresent disclosure demonstrates that the methods disclosed herein may beutilized to perform analyte concentration determinations that compensatefor or exhibit decreased sensitivity to such confounding variables.

FIG. 5 shows in greater detail a portion 700 of the signals illustratedin FIGS. 3-4. The closed circuit recovery potential 522 ramps toexcitation potential 523 over a rate controlled ramp potential 752 suchas, for example, a ramp rate of about 45 V/sec. Alternatively, the ramppotentials can be controlled to have a ramp rate less than about 50V/sec, between about 40 V/sec to about 50 V/sec, or between about 40V/sec to about 45 V/sec. Other embodiments control the ramp rate betweenpulses at different rates that are effective to reduce the contributionof the effect of capacitive charging on current responses.

The ramping rate of ramp potential 752 is effective to reduce the effectof capacitive charging on current response 762, which is generated inresponse to ramp potential 752 and excitation potential 523. Averagecurrent is measured starting about 30 msec after excitation potential523 is achieved over an about 100 msec measurement period ending at thepoint at which excitation potential 523 begins to ramp down to closedcircuit recovery potential 522 over ramp potential 753. Similar currentmeasurements may be taken for excitation current responses 621, 625,627, 629 and 631. It shall be appreciated that average currentmeasurements may be performed using continuous integration, discreteintegration, sampling or other averaging techniques. The successivecurrent measurements may be used to construct an effective current decaycurve from which analyte concentration can be calculated usingtechniques such as Cottrell analysis and others. In FIG. 5, ramppotential 753 is controlled to have a ramp rate substantially the sameas ramp potential 752. In other instances, ramp potential 753 may becontrolled at different rates or may be allowed to transition at asystem defined rate without active control.

Current responses, such as current responses 621-632, therefore encodeunique time ordered information relating to sample glucoseconcentration, sample Hct, sample temperature, as well as informationrelating to processes such as reagent wetting of the reagent, samplediffusion and separation with respect to the reagent, the establishmentof a stable glucose transport mechanism, and the kinetics associatedwith the reducible analyte. Pulse sequences such as pulse sequence 520provide short, distinct strobing of these processes with respect to timeand produces current responses including unique, time-orderedinformation relating to sample glucose concentration, sample Hct, sampletemperature, and other factors. The inventors have demonstrated a numberof unexpected advantages of the techniques disclosed herein throughexperiments in which pulse sequences such as pulse sequence 520 wereused to analyze various concentrations of blood glucose while Hct andtemperature were varied systematically.

FIG. 6 shows the effects of an exemplary systematic variation ofexcitation current responses and recovery current responses to pulsesequence 520 described above for varying Hct and constant temperature.Current responses are illustrated for four test samples with varying Hctconcentrations of about 29.5%, 40.5%, 54% and 69.5%, constant glucoseconcentrations of about 530 mg/dL, and constant temperatures of about25° C. The magnitude and decay rates of the excitation current responsesto excitation potential pulses 521, 523, 525, 527, 529 and 531 vary withsample Hct in a manner that is substantially constant with respect totime. At each Hct, current responses 801, 803, 805, 807, 809 and 811exhibit substantially consistent magnitudes and decay rates for eachpulse in pulse sequence 520. Within each pulse of pulse sequence 520,the magnitude of current responses 801, 803, 805, 807, 809 and 811varies in an inverse relationship with Hct.

The magnitude and growth rates of the recovery current responses torecovery potential pulses 522, 524, 526, 528, 530 and 532 also exhibitan observable relationship. Recovery current responses 802, 804, 806,808 and 810 to closed circuit recovery potential pulses 522, 524, 526,528, 530 and 532 have comparable starting magnitudes both within eachpulse and across pulses for each Hct, but have different rates of growthresulting in current response crossovers. As Hct varies, currentresponses 802, 804, 806, 808 and 810 grow at different rates dependingupon the Hct.

The aforementioned current response characteristics and relationshipsalso were demonstrated in experiments that used samples having constantglucose concentrations of about 33 mg/dL but were otherwisesubstantially in accordance with those described above.

In comparison, FIG. 7 shows the effects an exemplary systematicvariation of current responses to pulse sequence 520 for varyingtemperature, constant Hct and constant glucose concentration. Currentresponses are illustrated for five test samples with varyingtemperatures of 6.5° C., 12.5° C., 24.6° C., 32.4° C. and 43.7° C.,constant Hct of about 41%, and constant glucose concentrations of about535 mg/dL. The current responses to the positive DC potential of pulses521, 523, 525, 527, 529 and 531 show a relative decrease for successivepulses with respect to time. The magnitude of current responses 901,903, 905, 907, 909 and 911 decrease successively across pulses for eachof the sample temperatures. Furthermore, the amount of decrease acrosspulses varies depending upon sample temperature.

The magnitude and growth rates of the recovery current responses torecovery potential pulses 522, 524, 526, 528, 530 and 532 also exhibitan observable relationship. Recovery current responses to 522, 524, 526,528, 530 and 532 show substantially consistent magnitudes across pulsesand, within each pulse, have distinctly ordered starting values anddecreasing growth rates, but exhibit no crossover.

The aforementioned current response characteristics and relationshipsalso were demonstrated in experiments that used samples having constantglucose concentrations of about 33 mg/dL but were otherwisesubstantially in accordance with those described above.

From this research, a number of analyte concentration measurementmethods will now be described that use “descriptors” to encode magnitudeand shape information of excitation current responses and closed circuitrecovery current responses to the short duration pulse sequences ofexcitation potentials and closed circuit recovery potentials such asthose described above in, for example, FIGS. 3-5. Descriptors representa way to encode information relating to analyte concentration as well asinformation relating to systematic variation in confounding variablessuch as variation in sample Hct, sample temperature, sample salt,chemical kinetics, diffusion and other confounding variables. Suchinformation may be contained within magnitude and shape of currentresponses to short-duration excitation and recovery pulses, for example,as illustrated and described above in connection with FIGS. 6-7. Analyteconcentration determinations using descriptors provide a unique andunexpected compensation for insensitivity to the effects of confoundingvariables.

The descriptors described herein include (1) within-pulse descriptors,and (2) across-pulse descriptors. As used herein, “within-pulsedescriptor” or “within-pulse descriptors” means numerical quantitiesdetermined using one or more observed measurements within a currentresponse to an individual pulse (excitation or recovery) in a continuousDC waveform, to describe an intrinsic property of the current response.Two examples of within-pulse descriptors include the average currentvalue within a current response and the magnitude difference between twodifferent current responses separated in time during the same pulse(e.g., the first and last measured current values within a currentresponse). Additional examples of within-pulse descriptors include, butare not limited to, the slopes and intercepts from any two measurementpoints within a current response, for example, the first two points, thelast two points, the first and last points, and other sets of pointswithin a current response; the amplitudes and time constants from amulti-exponential fit of the current response using relative or absolutetime values; the sum of all current measurements and the cumulativeslope and intercept of those currents within a pulse, an angle between acertain portion of a current response and a horizontal or vertical axis;and extrapolated value from a certain portion of a current response.

As used herein, “across-pulse descriptor” or “across-pulse descriptors”means numerical quantities encoding information of the progression ordevelopment of current responses to two or more pulses as a function oftime. Across-pulse descriptors may encode information for currentresponses to sequential pulses or for pulses separated by interveningpulses or time. An example of an across-pulse descriptor includesmagnitude and/or slope differences for points or sets of points ofcurrent responses to two or more pulses, for example, the magnitudedifferences between the last current value in an excitation pulse andthe first current value in an adjacent recovery pulse, as well as themagnitude differences between the last point in a recovery pulse and thefirst point in the following excitation pulse. Additional examples ofacross-pulse descriptors include, but are not limited to, the currentresponses from all pulses, only positive pulses, only recovery pulses orother combinations, for example, the slope, intercept and/or parametervalues from a curve fit through the first or last current values fromall positive pulses or negative pulses, respectively.

Descriptors also may be used in connection with methods involvingtransformations of current response information. An ideal model of therelationship between current as a function of time and analyteconcentration is given by the Cottrell equation, which provides thatI=nFAc_(o)(D/πt)^(−1/2), where I is current in amps, n is the number ofelectrons to reduce/oxidize one molecule of a given analyte, F isFaraday's constant (96,485 C/mol), A is the area of a planar electrodein cm², c_(o) is the initial concentration of the analyte in mol/cm³,D=diffusion coefficient for the analyte in cm²/s, and t=time in sec. Asimplified form of the Cottrell equation is i=kt^(−1/2), where k is thecollection of constants n, F, A, c_(o) and D for a given system. TheCottrell equation is typically used to analyze graphs of current vs.time^(−1/2). For ideal Cottrell behavior, the resulting slope is linear,but this is not the case for many real world analyte measurementsystems.

As described above, descriptors encoding magnitude and shape informationof current responses such as slope, intercept and curvature information,can be utilized in performing analyte concentration determinations. Theinventors have developed data transformation methods that can beutilized in systems where Cottrell behavior is not linear. Certaintransformations utilize descriptors of the slope, linearity and/orcurvature in a transformed ln-ln space. Additional examples includeslopes and intercepts of best fit lines for two or more currentmeasurements, slopes and intercepts for current averages for rangeswithin pulses, and other types of slope and intercept descriptors.

FIG. 8 is a graph of current responses to recovery pulse 528 for foursamples 1001, 1002, 1003 and 1004 in a transformed coordinate systemwhere x=In(time) and y=In(current), time is measured from the start ofpulse 528, and current is measured at multiple points during pulse 528.Sample 1101 has a glucose concentration of 550 mg/dL, a Hctconcentration of 70%, and a temperature of 25° C. Sample 1102 has aglucose concentration of 550 mg/dL, a Hct concentration of 31%, and atemperature of 25° C. Sample 1103 has a glucose concentration of 550mg/dL, a Hct concentration of 42%, and a temperature of 44° C. Sample1104 has a glucose concentration of 550 mg/dL, a Hct concentration of42%, and a temperature of 6° C.

For recovery pulse 528, samples 1101, 1102, 1103 and 1104 show anonlinear relationship between In(current) and In(time) which includesinformation relating to sample temperature and sample Hct at a givenglucose concentration. For example, there is a systematic change in theseparation and order of current responses 1101 and 1102 resulting in acrossover as sample Hct changes and the sample temperature remainsconstant. In addition, there is a systematic difference in the slope andintercept defined by the last two current measurements for sample 1103and sample 1104 when the Hct level is constant and temperature isvaried. The descriptors disclosed herein may be used to encodeinformation of these systematic relationships and to perform analyteconcentration determinations compensating for variation in sample Hctand sample temperature among other confounding variables.

FIG. 9 is a graph of current responses to excitation pulse 529 forsamples 1101, 1102, 1103 and 1104 plotted in a transformed coordinatesystem where x=In(time) and y=In(current), time is measured from thestart of pulse 529, and current is measured at multiple points duringpulse 529. Samples 1101, 1102, 1103 and 1104 show a linear relationshipbetween In(current) and In(time) for excitation pulse 529 and therelative order of current responses remains constant during pulse 529.The effect of Hct variation can be seen through a comparison of samples1101 and 1102. The effect of temperature variation can be seen through acomparison of samples 1103 and 1104 and is greater than the effect dueto Hct variation. The descriptors disclosed herein may be used to encodeinformation of these systematic relationships and to perform analyteconcentration determinations compensating for variation in sample Hctand sample temperature among other confounding variables.

The descriptor and/or data transformation methods disclosed herein maybe used to determine glucose concentration in a sample of blood providedto a test cell including an electrode system. FIG. 10 illustrates anexemplary glucose concentration determination process 1200, which may beperformed using analyte measurement systems including a meter and anelectrochemical biosensor such as those described herein.

Process 1200 begins at operation 1210 where a meter is operativelycoupled with an electrochemical biosensor. Process 1200 continues tooperation 1212 where a sample is provided to the biosensor and contactedwith a reagent to provide a test cell including an electrode system inelectrical communication with the combined sample and reagent. Process1200 then continues to operation 1214 where a sample sufficiencydetermination is performed by the meter. If an affirmative samplesufficiency determination is made process 1200 proceeds to operation1216 and initiates a test signal and response measurement operation. Ifan affirmative sample sufficiency determination is not made, operation1214 repeats and may optionally time out or terminate after apredetermined number of attempts, or after a predetermined time haselapsed, or based upon other criteria.

Operation 1216 performs a test sequence and response measurementoperation during which a test sequence is generated by the meter andprovided to the electrode system of the test cell, and a response signalof the test cell is measured by the meter. In some instances, operation1216 generates and provides test sequence 500 to the electrode systemand measures the corresponding response 600. The measurement of response600 may include measurement of response component 610 and measurement ofcurrent responses 621-632. Multiple current measurements are takenduring each of current responses 621-632, and the measured currentinformation is stored in a memory. It shall be appreciated that in otherinstances, operation 1216 generates and provides other test signalsincluding a DC pulse sequence having excitation potential pulses andrecovery potential pulses and respective corresponding excitationcurrent responses and recovery current responses which may include thevariations and alternatives described herein above, as well as othernumbers, magnitudes and durations of excitation potential pulses andrecovery potential pulses. Process 1200 then proceeds to operation 1218,where a microcontroller and/or other processing circuitry processes thestored current measurement information to determine a glucoseconcentration.

Operation 1218 determines a glucose concentration based upon the storedcurrent measurement information including current response informationcorresponding to excitation potential pulses and current responseinformation corresponding to recovery pulses. In some instances,operation 1218 utilizes descriptors that encode the slope and interceptof the last two current measurement points within a current response inan x-y coordinate system where x=In(time) and y=In(current) and wheretime is measured relative to an identified starting point for each pulse(excitation and recovery) to determine an effective DC current accordingto Equation 1:

$I_{eff} = {\sum\limits_{i = 1}^{i = N}{\left( {{c_{i,m}*P_{i,m}} + {c_{i,b}*P_{i,b}}} \right).}}$

In Equation 1, I_(eff) designates the effective DC current, i designatesa pulse number in a pulse sequence of the excitation potential pulsesand the recovery potential pulses, N designates the total number ofpulses in a sequence (including both excitation and recovery pulses),P_(i,m) is a descriptor designating the slope of the last two currentmeasurement points within a pulse in an x-y coordinate system wherex=In(time) and y=In(current), P_(i,b) is a descriptor designating theintercept of the last two current measurement points within a pulse inan x-y coordinate system where x=In(time) and y=In(current), c_(i,m)designates a slope weighting constant, and c_(i,b) designates anintercept weighting constant. The weighting constants may be determinedempirically using a number of optimization techniques, for example,those available in the SAS software package available from SASInstitute, Inc.

It shall be appreciated that the number of pulses and associated currentresponses may vary. In some examples herein, the number of pulses wasN=9. Other forms, however, can use a different numbers of pulses.Furthermore, it shall be appreciated that not all pulses in a testsequence need be utilized in an analyte concentration determination, forexample, where the number of pulses N=9, and pulse sequence includingeleven pulses such as that disclosed above in connection with FIG. 3 maybe used, and the current response information for pulses 10 and 11 maynot be utilized. In other instances, information from current responsesto all pulses in a test signal may be used.

Operation 1218 uses the effective current I_(eff) as well as AC currentresponse information to determine a predicted glucose concentrationaccording to Equation 2:Predglu=a0+(b0+exp(bl+b2*I _(eff) +P _(eff) +Y _(eff)))*(I _(eff)).

In Equation 2, P_(eff) is the effective phase of the AC currentresponse, Y_(eff) is the effective admittance of the AC currentresponse, and a0, b0, b1 and b2 are constants that are determinedthrough known optimization techniques. The phase term, P_(eff), isdetermined according to Equation 3:P _(eff) =bp2*(p11*cos(α)+p12*sin(α))+bp3*(−p11*sin(α)+p12*cos(α)).

In Equation 3, α=arctan(I), p11 is a 20 kHz AC current response phase,p12 is a 10 kHz AC current response phase, and bp2 and bp3 are optimizedweighting coefficients that may be determined by various optimizationtechniques. The admittance term, Y_(eff), is defined according toEquation 4:Y _(eff) =by2*(y11*cos(α)+y12*sin(α))+by3*(−y11*sin(α)+y12*cos(α)).

In Equation 4, α=arctan(I), and y11 is a 20 kHz AC admittance, y12 is a10 kHz AC admittance, and by2 and by3 are optimized weightingcoefficients that may be determined by various optimization techniques.

Operation 1218 may use alternative methods to determine a predictedglucose concentration, for example, according to relationship describedby Equation 5:Predglu=a0+a1*I _(eff)+exp(b0+P _(eff) +Y _(eff))*I _(eff).

In Equation 5, P_(eff) is the effective phase of the AC currentresponse, Y_(eff) is the effective admittance of the AC currentresponse, and a0, a1 and b0 are constants. P_(eff) and Y_(eff) may bedetermined using substantially the same techniques as described above.

It shall be appreciated that the descriptors, transformations anddeterminations described above in connection with operation 1218 arenon-limiting examples of methods by which analyte concentrations can bedetermined using information included in current responses correspondingto a DC pulse sequence comprising excitation potential pulses andcurrent response information for recovery pulses. Alternative methodsincorporating the inventive concept may utilize a variety of additionalor alternate descriptors and/or data transformations in accordance withthe principles and examples disclosed herein.

The inventors developed and experimentally validated that a number ofunexpected performance characteristics can be achieved through themethods disclosed herein. A number of such performance characteristicswere validated in connection with the general method described inconnection with FIG. 10. An exemplary performance characteristicincludes 10/10 performance, where less than 5% of glucose determinationsperformed using a plurality of test elements included an error greaterthan ±10% at high glucose levels such as those at or above 75 mg/dLand/or an error of ±10 mg/dL at low glucose levels such as those below75 mg/dL.

Certain exemplary methods therefore include 10/10 performance forvariation in sample temperature, variation in sample Hct, and/orvariation in sample salt. Some methods include 10/10 performance for 50%variation in sample Hct, for example, variation from 20%-70% Hct. Othermethods include 10/10 performance for 50° C. variation in sampletemperature, for example, variation from 6° C. to 44° C. Other methodsinclude 10/10 performance for 40 mg/dL variation in sample salt, forexample, variation in sample salt from 140 mg/dL to 180 mg/dL. Othermethods include 10/10 performance for a combination of the foregoingtemperature, Hct and/or salt variations.

Further exemplary performance characteristics include, but are notlimited to, measurement bias, normalized error (“NE”) standard deviationof normalized error (“SDNE”), total system error (“TSE”) andcombinations thereof. In one exemplary validation study, 10/10performance for compensation for co-variation of sample Hct from about20% to about 70% and sample temperature from about 6° C. to about 44° C.demonstrated the performance characteristics summarized in Table 1below.

TABLE 1 10/10 Temperature 10/10 Hct Bias at Failures Failures Nominal NESDNE TSE 0 0 1.79 0.22 5.67 9.55

Another exemplary performance characteristic includes bias, SDNE and TSEcharacteristics for variation in reagent film thickness. In an exemplaryvalidation study, three rounds of testing were performed with capillaryblood for three rolls of test elements produced on up to two differentlanes (O and M). Measured dry reagent film thicknesses for rolls 1, 2and 3 were 4.64, 4.08 and 5.10 μm, which correspond to nominal, −12%,+10%. The performance characteristics for this study are summarized inTable 2 below.

TABLE 2 Roll Lane N Mean Bias SDNE TSE 1 M 477 −0.30 4.11 8.52 1 O 233−1.68 4.22 10.12 1 M&O 710 −0.75 4.20 9.14 2 O 236 6.17 5.49 17.15 3 M234 −6.32 4.39 15.10

The study demonstrated a negligible bias (−0.75) with capillary blood,even though the analyte concentration technique was not trained withcapillary blood. The study also demonstrated low mean biases for bothlanes of roll 1 even though the algorithm was trained with strips fromlane M only. The study further demonstrate insensitivity to coat weightvariation as the mean bias was about +6% at the lower coat weight andabout −6% at the higher coat weight.

In another exemplary validation study, three rounds of testing wereperformed on the test elements from roll 1. This study consideredstudy-to-study variation in testing and demonstrated the resultssummarized in Table 3 below.

TABLE 3 Roll Lane N Mean Bias SDNE TSE 1 M 238 0.06 3.85 7.76 1 O 2390.05 4.09 8.23 1 M&O 477 0.06 3.97 7.99

A further exemplary validation study tested ten different lots of testelements, three of which were used in verification of the analyteconcentration determination technique. This study demonstratedlot-to-lot robustness results summarized in Table 4 below.

TABLE 4 Roll Lane N Mean Bias SDNE TSE 2 M&O 480 −0.73 4.44 9.61 3 M&O479 2.31 3.78 9.88 4 M&O 478 2.44 4.33 11.10 2 M 240 0.57 4.54 9.66 2 O240 −2.04 3.93 9.9 3 M 240 2.68 3.55 9.78 3 O 239 1.94 3.97 9.89 4 M 2401.91 4.05 10.02 4 O 238 2.98 4.53 12.04

Another exemplary performance characteristic includes compensation fordose tremble such as double dosing or delayed dosing at various glucoseconcentrations and Hct levels. An exemplary dose tremble validationstudy was conducted and demonstrated the results summarized in Table 5below.

TABLE 5 Mean Standard Glucose HCT Dose Type Prediction Deviation Bias120 45 Normal 135.22 3.65 0.00 120 45 Tremble 138.24 4.18 2.23 120 70Normal 124.38 3.88 0.00 120 70 Tremble 127.72 3.79 2.68 550 45 Normal578.03 3.35 0.00 550 45 Tremble 593.94 3.37 2.75 550 70 Normal 621.513.70 0.00 550 10 Tremble 626.13 4.23 0.74

Performance characteristics also were validated in connection with thedescriptors and method described in connection with FIG. 10, as well asadditional descriptors. The performance characteristics for a variety ofexemplary descriptors are summarized in Table 6 below.

TABLE 6 Descriptors Rate of Total LN Time, LN Simple 1/sqrt Time Charge(Q) All Pulse Current Linear, R's with Buildup - Transitions -Descriptors Compensated Temperature Orig DC, Rs Orig DC of FIG. 10 AC &DC Descriptors Modified Y's Current Failed T 0 0 0 0 0 Claims Failed Hct0 0 0 0 3 Claims SDNE 4.7 3.7 3.7 8.0 6.5 Training Salt Claim PassedPassed Passed Passed Passed Mean Bias −0.7 −0.1 0.6 −0.6 −5.2 CV Round 1SDNE 4.2 4.7 4.7 4.9 4.3 Round 1 Mean Bias 0.1 0.1 1.6 −1.1 −5.8 CVRound 2 SDNE 4.0 4.4 4.1 7.1 5.9 Round 2 Mean Bias 2.3 3.3 −3.1 −3.9−3.1 CV Round 3 SDNE 3.8 4.3 3.7 5.1 4.6 Round 3 Side Dosing 0.6 3.2 2.40.8 1.4 Bias 5 mg/dL 8.4 24.5 17.0 1.8 0.3 Ascorbic Acid Bias at 40 Glu15 mg/dL 34.2 59.5 53.4 18.1 −1.7 Ascorbic Acid Bias at 40 Glu

All of the patents, patent applications, patent application publicationsand other publications recited herein are hereby incorporated byreference as if set forth in their entirety.

The present inventive concept has been described in connection with whatare presently considered to be the most practical and preferredembodiments. However, the inventive concept has been presented by way ofillustration and is not intended to be limited to the disclosedembodiments. Accordingly, one of skill in the art will realize that theinventive concept is intended to encompass all modifications andalternative arrangements within the spirit and scope of the inventiveconcept as set forth in the appended claims.

The invention claimed is:
 1. A method of electrochemically measuringglucose concentration in a fluid sample, the method comprising the stepsof: applying an electrical test sequence to an electrochemicalbiosensor, the biosensor comprising: an electrode system, a reagent inelectrical communication with the electrode system, and a receptacleconfigured to contact the fluid sample provided to the biosensor, withthe fluid sample in fluidic contact with the reagent, wherein the testsequence comprises at least one DC block, the at least one DC blockincludes at least one excitation potential pulse and at least onerecovery potential pulse, each potential configured to produce responseinformation to the test sequence, and wherein a closed circuit conditionof the electrode system is maintained during the at least one DC block;measuring the response information from the test sequence; anddetermining the glucose concentration of the fluid sample based at leastin part upon descriptors built from encoded magnitude and shapecharacteristics of the response information to the test sequence,wherein the descriptors encode transformed excitation current responseinformation and transformed recovery current response information, andwherein the determining is further based at least in part upon thetransformed excitation current response information and the transformedrecovery current response information.
 2. The method of claim 1 furthercomprising the step of transforming the excitation current responseinformation and the recovery current response information from a firstx-y space, where x=time and y=current to a second x-y space wherex=In(time) and y=In(current).
 3. The method of claim 1, wherein thedetermining the glucose concentration step is based upon an effectivecurrent determined based upon the transformed excitation currentresponse information and the transformed recovery current responseinformation.
 4. The method of claim 3, wherein the determined glucoseconcentration is a predicted glucose concentration, Predglu, determinedin accordance with the equation:Predglu=a0+(b0+exp(b1+b2*I_(eff)+P_(eff)+Y_(eff)))*(I_(eff)), where a0,b0, b1, and b2 are constants, P_(eff) is an effective phase and Y_(eff)is an effective admittance, wherein P_(eff) is determined in accordancewith the equation:P_(eff)=bp2*(p11*cos(α)+p12*sin(α))+bp3*(−p11*sin(α)+p12*cos(α)), whereα=arctan(1), p11 is a 20 kHz AC phase, p12 is a 10 kHz AC phase, and bp2and bp3 are weighting terms, and wherein Y_(eff) is determined inaccordance with the equation:Y_(eff)=by2*(y11*cos(α)+y12*sin(α))+by3*(−y11*sin(α)+y12*cos(α)), whereα=arctan(1), y11 is a 20 kHz AC admittance, y12 is a 10 kHz ACadmittance, and by2 and by3 are weighting terms.
 5. The method of claim1, wherein 95% of the determined glucose concentrations fall within ±10mg/dl of a reference at concentrations less than about 75 mg/dL, andwherein 95% of the determined glucose concentrations fall within ±10% ofthe reference at concentrations greater than or equal to about 75 mg/dL.6. The method of claim 1, wherein the determined glucose concentrationhas a standard deviation of normalized error (SDNE) of 5% or less. 7.The method of claim 1, wherein the determined glucose concentration hasa total system error (TSE) of 10% or less.